A key result in entanglement theory is that the addition of a catalyst dramatically enlarges the set of possible state transformations via local operations and classical communication (LOCC). However, it remains unclear what is the interplay between classical communication and quantum catalysis. Here our aim is to disentangle the effect of the catalyst from that of classical communication. To do so, we explore a class of state transformations termed catalytic local operations (CLO) and compare it to LOCC and to stochastic LOCC augmented by bounded quantum communication. We show that these classes are incomparable and capture different facets of quantum state transformations.
A key result in entanglement theory is that the addition of a catalyst dramatically enlarges the set of possible state transformations via local operations and classical communication (LOCC). However, it remains unclear what is the interplay between classical communication and quantum catalysis. Here our aim is to disentangle the effect of the catalyst from that of classical communication. To do so, we explore a class of state transformations termed catalytic local operations (CLO) and compare it to LOCC and to stochastic LOCC augmented by bounded quantum communication. We show that these classes are incomparable and capture different facets of quantum state transformations.
Abstract Conversion of entangled states under ( s tochastic) local operations and classical communication ((S)LOCC) admits the phenomenon of catalysis. Here we explore the possibility of a copy of the initial state itself performing as a catalyst, which we call a self-catalytic process. We show explicit examples of self-catalysis. Necessary and sufficient conditions for the phenomenon to take place are discussed. We numerically estimate how frequent it is and we show that increasing the number of copies used as catalyst can increase the probability of conversion, but does not make the process deterministic. By the end we conjecture that under LOCC the probability of finding a self-catalytic reaction does not increase monotonically with the dimensions whereas under SLOCC, it does increase.
The correlations of certain entangled states can be perfectly simulated classically via a local model. Hence such states are termed Bell local, as they cannot lead to Bell inequality violation. Here, we show that Bell nonlocality can nevertheless be activated for certain Bell-local states via a catalytic process. Specifically, we present a protocol where a Bell-local state, combined with a catalyst, is transformed into a Bell-nonlocal state while the catalyst is returned exactly in its initial state. Importantly, this transformation is deterministic and based only on local operations. Moreover, this procedure is possible even when the state of the catalyst is itself Bell local, demonstrating a new form of superactivation of Bell nonlocality, as well as an interesting form of quantum catalysis. On the technical level, our main tool is a formal connection between catalytic activation and many-copy activation.
Given a finite-dimensional pure state transformation restricted by entanglement-assisted local operations and classical communication (ELOCC), we derive minimum and maximum bounds on the entanglement of an ancillary catalyst that allows that transformation. These bounds are nontrivial even when the Schmidt number of both the original and ancillary states becomes large. We identify a lower bound for the dimension of a catalyst allowing a particular ELOCC transformation. Along with these bounds, we present further constraints on ELOCC transformations by identifying restrictions on the Schmidt coefficients of the target state. In addition, an example showing the existence of qubit ELOCC transformations with multiple ranges of potential ancillary states is provided. This example reveals some additional difficulty in finding strict bounds on ELOCC transformations, even in the qubit case. Finally, a comparison of the bounds in this paper with previously discovered bounds is presented.
Understanding the fundamental limits of state convertibility is crucial for establishing the boundaries of quantum information processing and thermodynamic efficiency. While auxiliary systems, catalysts, can facilitate otherwise impossible transformations, standard catalysis rigidly requires the auxiliary system to return to its exact initial state. In this work, we investigate the power of flexible catalysis, where the catalyst evolves through a cycle of states, restoring its initial configuration only after a finite number of steps. Focusing on the regime of fixed, finite dimensions, we analyze the capabilities of flexible catalysis within the resource theories of entanglement and quantum thermodynamics. In the context of entanglement, we derive conditions limiting flexible catalysts, yet show that flexible catalysis can be strictly more powerful than same-dimensional standard catalysis: it enables deterministic transformations achievable by no standard catalyst of the same dimension, and it strictly increases the success probability of stochastic local operations and classical communication. A similar deterministic advantage arises in quantum thermodynamics, where flexible catalysis enables state transformations that are impossible with any standard catalyst of fixed dimension and Hamiltonian but become achievable via flexible catalysis.
The distribution of typical bipartite pure states is studied within the framework of state transformation via local operations and classical communication (LOCC). We report the statistics of comparable and incomparable states in different dimensions for single- and multicopy regimes, and we establish a connection between state transformation and the difference between the entanglement contents of the initial and the target states. From the analysis of catalyst resources, required to further otherwise impossible LOCC transformations between pairs, we demonstrate a universal pattern in the average and minimum entanglement of the randomly generated catalysts. Furthermore, we introduce a concept of hierarchy between different kinds of catalysts, and we show how they can not only aid in the conversion of incomparable states, but they can also act as a less costly resource toward this goal. We confirm the existence of catalysts, referred to as strong catalysts, which can activate LOCC transformation between pairs at the single-copy level, when it is initially impossible even with multiple copies.
Quantum catalysts can overcome otherwise impossible quantum state transformations without being consumed, and allowing them to become correlated with the output makes this assistance substantially more powerful. This raises a fundamental question for entanglement theory: which limitations on state manipulation remain when such correlated catalysts are freely available? We answer this question in the positive-partial-transpose (PPT) resource theory, which allows a substantially broader class of operations than local operations and classical communication (LOCC). We identify general conditions under which regularized relative-entropy measures become strongly superadditive, and use them to construct monotones that constrain correlated catalytic PPT transformations without any knowledge of the catalyst. In particular, we prove that the regularized PPT relative entropy is fully additive and strongly superadditive, resolving an open problem in entanglement theory. Most importantly, these constraints show that even arbitrary correlated catalysts cannot restore asymptotic reversibility: for an explicit state, the optimal entanglement distillation rate remains strictly smaller than the entanglement cost. Thus, substantial catalytic assistance does not remove some of the fundamental limitations of mixed-state entanglement manipulation.